A Finite-Sample Deviation Bound for Stable Autoregressive Processes
This provides theoretical guarantees for parameter estimation in time-series models, but it is incremental as it builds on existing concentration methods.
The paper tackles the problem of deriving non-asymptotic deviation bounds for least squares estimators in Gaussian autoregressive processes, resulting in a finite-time bound on deviation probability for estimated parameters.
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $χ^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR$(n)$ process. We discuss extensions and limitations of our approach.